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Basic Concepts in Signals and Systems Read chapter Read first chapter

2018 | OriginalPaper | Chapter

15. Perfect Transformer, Current Discontinuity and Degeneracy

Author : Suhash Chandra Dutta Roy

Published in: Circuits, Systems and Signal Processing

Publisher: Springer Singapore

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Abstract

That on connecting a source in the primary circuit of a perfectly coupled transformer, the currents in both the primary and secondary coils may be discontinuous does not appear to have been widely discussed in the literature. In this discussion, we present an analysis of the general circuit and show that in general, the currents will be discontinuous, except for specific combinations of the initial currents in the two coils. Although unity coupling coefficient cannot be realized in practice, a perfectly coupled transformer is a useful concept in circuit analysis and synthesis, and the results presented here should be of interest to students as well as teachers of circuit theory.

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Appendix
Available only for authorised users
Footnotes
1
This ‘equivalent’ circuit implies only mathematical equivalence (of the loop equations) but not physical equivalence, because the two coils have no common point.
 
2
Notably, in [2], there are no examples or discussions on initial conditions in coupled coils. In the only example in which a coupled coil appears (pp 110–112), inductor junctions are created through additional inductors in each circuit and a current generator in the secondary circuit.
 
3
Kuo [1], at this point, assumes i 1(0–) = i 2(0–), presumably, as an example. We give general results in Eqs. 15.25 and 15.26.
 
Literature
1.
F.F. Kuo, Network Analysis and Synthesis (John Wiley, New York, 1966), pp. 123–126
2.
S. Seshu, N. Balabanian, Linear Network Analysis (John Wiley, New York, 1963), pp. 101–112
Metadata
Title
Perfect Transformer, Current Discontinuity and Degeneracy
Author
Suhash Chandra Dutta Roy
Copyright Year
2018
Publisher
Springer Singapore
Book
Circuits, Systems and Signal Processing

Print ISBN: 978-981-10-6918-5

Electronic ISBN: 978-981-10-6919-2

Copyright Year: 2018

DOI
https://doi.org/10.1007/978-981-10-6919-2_15